\(\renewcommand{\hat}[1]{\widehat{#1}}\)

Shared Qs (021)


  1. Question

    Does the complex number \(z=3+6i\) solve the equation below?

    \[z^2-6z+47=0\]


    1. Yes
    2. No

    Solution


  2. Question

    Does the complex number \(z=5-3i\) solve the equation below?

    \[z^2-10z+34=0\]


    1. Yes
    2. No

    Solution


  3. Question

    Does the complex number \(z=-2-8i\) solve the equation below?

    \[z^2+3z+72=0\]


    1. Yes
    2. No

    Solution


  4. Question

    Does the complex number \(z=-7-9i\) solve the equation below?

    \[z^2+15z+127=0\]


    1. Yes
    2. No

    Solution


  5. Question

    Does the complex number \(z=-2-4i\) solve the equation below?

    \[z^2+4z+20=0\]


    1. Yes
    2. No

    Solution


  6. Question

    Does the complex number \(z=-4-6i\) solve the equation below?

    \[z^2+9z+50=0\]


    1. Yes
    2. No

    Solution


  7. Question

    Does the complex number \(z=6-8i\) solve the equation below?

    \[z^2-12z+104=0\]


    1. Yes
    2. No

    Solution


  8. Question

    Does the complex number \(z=8-3i\) solve the equation below?

    \[z^2-16z+73=0\]


    1. Yes
    2. No

    Solution


  9. Question

    Does the complex number \(z=3+9i\) solve the equation below?

    \[z^2-6z+82=0\]


    1. Yes
    2. No

    Solution


  10. Question

    Does the complex number \(z=-7-8i\) solve the equation below?

    \[z^2+14z+113=0\]


    1. Yes
    2. No

    Solution


  11. Question

    A student has taken 6 exams and gotten an average of 72. What score does the student need on the next exam to bring the average to 75? (All exams are equally weighted in the average.)


    Solution


  12. Question

    A student has taken 3 exams and gotten an average of 72. What score does the student need on the next exam to bring the average to 75? (All exams are equally weighted in the average.)


    Solution


  13. Question

    A student has taken 5 exams and gotten an average of 66.6. What score does the student need on the next exam to bring the average to 70? (All exams are equally weighted in the average.)


    Solution


  14. Question

    A student has taken 5 exams and gotten an average of 66. What score does the student need on the next exam to bring the average to 70? (All exams are equally weighted in the average.)


    Solution


  15. Question

    A student has taken 4 exams and gotten an average of 63.5. What score does the student need on the next exam to bring the average to 70? (All exams are equally weighted in the average.)


    Solution


  16. Question

    A student has taken 4 exams and gotten an average of 75.5. What score does the student need on the next exam to bring the average to 80? (All exams are equally weighted in the average.)


    Solution


  17. Question

    A student has taken 5 exams and gotten an average of 82.2. What score does the student need on the next exam to bring the average to 85? (All exams are equally weighted in the average.)


    Solution


  18. Question

    A student has taken 7 exams and gotten an average of 62. What score does the student need on the next exam to bring the average to 65? (All exams are equally weighted in the average.)


    Solution


  19. Question

    A student has taken 4 exams and gotten an average of 61.5. What score does the student need on the next exam to bring the average to 65? (All exams are equally weighted in the average.)


    Solution


  20. Question

    A student has taken 3 exams and gotten an average of 61. What score does the student need on the next exam to bring the average to 70? (All exams are equally weighted in the average.)


    Solution


  21. Question

    A lifeguard wants to get to a struggling swimmer as soon as possible. The lifeguard can run along the beach at 3.7 m/s and swim at 1.6 m/s. The lifeguard will run \(x\) meters and swim \(\sqrt{(170-x)^2+20^2}\) meters.

    plot of chunk unnamed-chunk-2

    Thus, the time is a function of \(x\).

    \[t(x) ~=~ \frac{x}{3.7} + \frac{\sqrt{(170-x)^2+20^2}}{1.6}\]

    Find the value of \(x\) (in meters) that minimizes the amount of time. The tolerance is \(\pm 0.1\) meters.


    Solution


  22. Question

    A lifeguard wants to get to a struggling swimmer as soon as possible. The lifeguard can run along the beach at 3 m/s and swim at 0.9 m/s. The lifeguard will run \(x\) meters and swim \(\sqrt{(130-x)^2+30^2}\) meters.

    plot of chunk unnamed-chunk-2

    Thus, the time is a function of \(x\).

    \[t(x) ~=~ \frac{x}{3} + \frac{\sqrt{(130-x)^2+30^2}}{0.9}\]

    Find the value of \(x\) (in meters) that minimizes the amount of time. The tolerance is \(\pm 0.1\) meters.


    Solution


  23. Question

    A lifeguard wants to get to a struggling swimmer as soon as possible. The lifeguard can run along the beach at 4 m/s and swim at 1.8 m/s. The lifeguard will run \(x\) meters and swim \(\sqrt{(290-x)^2+10^2}\) meters.

    plot of chunk unnamed-chunk-2

    Thus, the time is a function of \(x\).

    \[t(x) ~=~ \frac{x}{4} + \frac{\sqrt{(290-x)^2+10^2}}{1.8}\]

    Find the value of \(x\) (in meters) that minimizes the amount of time. The tolerance is \(\pm 0.1\) meters.


    Solution


  24. Question

    A lifeguard wants to get to a struggling swimmer as soon as possible. The lifeguard can run along the beach at 2.1 m/s and swim at 1.2 m/s. The lifeguard will run \(x\) meters and swim \(\sqrt{(180-x)^2+60^2}\) meters.

    plot of chunk unnamed-chunk-2

    Thus, the time is a function of \(x\).

    \[t(x) ~=~ \frac{x}{2.1} + \frac{\sqrt{(180-x)^2+60^2}}{1.2}\]

    Find the value of \(x\) (in meters) that minimizes the amount of time. The tolerance is \(\pm 0.1\) meters.


    Solution


  25. Question

    A lifeguard wants to get to a struggling swimmer as soon as possible. The lifeguard can run along the beach at 3.5 m/s and swim at 1.2 m/s. The lifeguard will run \(x\) meters and swim \(\sqrt{(300-x)^2+60^2}\) meters.

    plot of chunk unnamed-chunk-2

    Thus, the time is a function of \(x\).

    \[t(x) ~=~ \frac{x}{3.5} + \frac{\sqrt{(300-x)^2+60^2}}{1.2}\]

    Find the value of \(x\) (in meters) that minimizes the amount of time. The tolerance is \(\pm 0.1\) meters.


    Solution


  26. Question

    A lifeguard wants to get to a struggling swimmer as soon as possible. The lifeguard can run along the beach at 3.7 m/s and swim at 1 m/s. The lifeguard will run \(x\) meters and swim \(\sqrt{(250-x)^2+50^2}\) meters.

    plot of chunk unnamed-chunk-2

    Thus, the time is a function of \(x\).

    \[t(x) ~=~ \frac{x}{3.7} + \frac{\sqrt{(250-x)^2+50^2}}{1}\]

    Find the value of \(x\) (in meters) that minimizes the amount of time. The tolerance is \(\pm 0.1\) meters.


    Solution


  27. Question

    A lifeguard wants to get to a struggling swimmer as soon as possible. The lifeguard can run along the beach at 3.7 m/s and swim at 1.8 m/s. The lifeguard will run \(x\) meters and swim \(\sqrt{(280-x)^2+40^2}\) meters.

    plot of chunk unnamed-chunk-2

    Thus, the time is a function of \(x\).

    \[t(x) ~=~ \frac{x}{3.7} + \frac{\sqrt{(280-x)^2+40^2}}{1.8}\]

    Find the value of \(x\) (in meters) that minimizes the amount of time. The tolerance is \(\pm 0.1\) meters.


    Solution


  28. Question

    A lifeguard wants to get to a struggling swimmer as soon as possible. The lifeguard can run along the beach at 3.9 m/s and swim at 1.3 m/s. The lifeguard will run \(x\) meters and swim \(\sqrt{(240-x)^2+30^2}\) meters.

    plot of chunk unnamed-chunk-2

    Thus, the time is a function of \(x\).

    \[t(x) ~=~ \frac{x}{3.9} + \frac{\sqrt{(240-x)^2+30^2}}{1.3}\]

    Find the value of \(x\) (in meters) that minimizes the amount of time. The tolerance is \(\pm 0.1\) meters.


    Solution


  29. Question

    A lifeguard wants to get to a struggling swimmer as soon as possible. The lifeguard can run along the beach at 3.9 m/s and swim at 1.1 m/s. The lifeguard will run \(x\) meters and swim \(\sqrt{(170-x)^2+30^2}\) meters.

    plot of chunk unnamed-chunk-2

    Thus, the time is a function of \(x\).

    \[t(x) ~=~ \frac{x}{3.9} + \frac{\sqrt{(170-x)^2+30^2}}{1.1}\]

    Find the value of \(x\) (in meters) that minimizes the amount of time. The tolerance is \(\pm 0.1\) meters.


    Solution


  30. Question

    A lifeguard wants to get to a struggling swimmer as soon as possible. The lifeguard can run along the beach at 3.3 m/s and swim at 1.6 m/s. The lifeguard will run \(x\) meters and swim \(\sqrt{(240-x)^2+30^2}\) meters.

    plot of chunk unnamed-chunk-2

    Thus, the time is a function of \(x\).

    \[t(x) ~=~ \frac{x}{3.3} + \frac{\sqrt{(240-x)^2+30^2}}{1.6}\]

    Find the value of \(x\) (in meters) that minimizes the amount of time. The tolerance is \(\pm 0.1\) meters.


    Solution


  31. Question

    The figure below summarizes the empirical rule. If a normally-distributed population has a mean length of \(\mu=800\) cm and a standard deviation of \(\sigma=15\) cm, then what is the probability an individual has a length between 785 cm and 830 cm?

    The tolerance is \(\pm 0.01\) cm.

    plot of chunk unnamed-chunk-2


    Solution


  32. Question

    The figure below summarizes the empirical rule. If a normally-distributed population has a mean length of \(\mu=750\) cm and a standard deviation of \(\sigma=20\) cm, then what is the probability an individual has a length between 690 cm and 750 cm?

    The tolerance is \(\pm 0.01\) cm.

    plot of chunk unnamed-chunk-2


    Solution


  33. Question

    The figure below summarizes the empirical rule. If a normally-distributed population has a mean length of \(\mu=250\) cm and a standard deviation of \(\sigma=5\) cm, then what is the probability an individual has a length between 240 cm and 260 cm?

    The tolerance is \(\pm 0.01\) cm.

    plot of chunk unnamed-chunk-2


    Solution


  34. Question

    The figure below summarizes the empirical rule. If a normally-distributed population has a mean length of \(\mu=300\) cm and a standard deviation of \(\sigma=30\) cm, then what is the probability an individual has a length between 300 cm and 360 cm?

    The tolerance is \(\pm 0.01\) cm.

    plot of chunk unnamed-chunk-2


    Solution


  35. Question

    The figure below summarizes the empirical rule. If a normally-distributed population has a mean length of \(\mu=700\) cm and a standard deviation of \(\sigma=2\) cm, then what is the probability an individual has a length between 698 cm and 702 cm?

    The tolerance is \(\pm 0.01\) cm.

    plot of chunk unnamed-chunk-2


    Solution


  36. Question

    The figure below summarizes the empirical rule. If a normally-distributed population has a mean length of \(\mu=300\) cm and a standard deviation of \(\sigma=25\) cm, then what is the probability an individual has a length between 250 cm and 375 cm?

    The tolerance is \(\pm 0.01\) cm.

    plot of chunk unnamed-chunk-2


    Solution


  37. Question

    The figure below summarizes the empirical rule. If a normally-distributed population has a mean length of \(\mu=600\) cm and a standard deviation of \(\sigma=2\) cm, then what is the probability an individual has a length between 594 cm and 606 cm?

    The tolerance is \(\pm 0.01\) cm.

    plot of chunk unnamed-chunk-2


    Solution


  38. Question

    The figure below summarizes the empirical rule. If a normally-distributed population has a mean length of \(\mu=200\) cm and a standard deviation of \(\sigma=5\) cm, then what is the probability an individual has a length between 190 cm and 195 cm?

    The tolerance is \(\pm 0.01\) cm.

    plot of chunk unnamed-chunk-2


    Solution


  39. Question

    The figure below summarizes the empirical rule. If a normally-distributed population has a mean length of \(\mu=450\) cm and a standard deviation of \(\sigma=20\) cm, then what is the probability an individual has a length between 490 cm and 510 cm?

    The tolerance is \(\pm 0.01\) cm.

    plot of chunk unnamed-chunk-2


    Solution


  40. Question

    The figure below summarizes the empirical rule. If a normally-distributed population has a mean length of \(\mu=650\) cm and a standard deviation of \(\sigma=15\) cm, then what is the probability an individual has a length between 620 cm and 665 cm?

    The tolerance is \(\pm 0.01\) cm.

    plot of chunk unnamed-chunk-2


    Solution


  41. Question

    Below is a 2-way table expressing joint probabilities.

    A not A
    B 33% 42%
    not B 11% 14%

    So,

    \[\begin{align} P(A \text{ and }B) &= 0.33 \\ P(A \text{ and not }B) &= 0.11 \\ P([\text{not }A] \text{ and }B) &= 0.42 \\ P([\text{not }A] \text{ and [not }B]) &= 0.14 \\ \end{align}\]

    Are events \(A\) and \(B\) independent?


    1. Yes, events A and B are independent.
    2. No, events A and B are dependent.

    Solution


  42. Question

    Below is a 2-way table expressing joint probabilities.

    A not A
    B 27% 48%
    not B 9% 16%

    So,

    \[\begin{align} P(A \text{ and }B) &= 0.27 \\ P(A \text{ and not }B) &= 0.09 \\ P([\text{not }A] \text{ and }B) &= 0.48 \\ P([\text{not }A] \text{ and [not }B]) &= 0.16 \\ \end{align}\]

    Are events \(A\) and \(B\) independent?


    1. Yes, events A and B are independent.
    2. No, events A and B are dependent.

    Solution


  43. Question

    Below is a 2-way table expressing joint probabilities.

    A not A
    B 7% 13%
    not B 28% 52%

    So,

    \[\begin{align} P(A \text{ and }B) &= 0.07 \\ P(A \text{ and not }B) &= 0.28 \\ P([\text{not }A] \text{ and }B) &= 0.13 \\ P([\text{not }A] \text{ and [not }B]) &= 0.52 \\ \end{align}\]

    Are events \(A\) and \(B\) independent?


    1. Yes, events A and B are independent.
    2. No, events A and B are dependent.

    Solution


  44. Question

    Below is a 2-way table expressing joint probabilities.

    A not A
    B 33% 28%
    not B 17% 22%

    So,

    \[\begin{align} P(A \text{ and }B) &= 0.33 \\ P(A \text{ and not }B) &= 0.17 \\ P([\text{not }A] \text{ and }B) &= 0.28 \\ P([\text{not }A] \text{ and [not }B]) &= 0.22 \\ \end{align}\]

    Are events \(A\) and \(B\) independent?


    1. Yes, events A and B are independent.
    2. No, events A and B are dependent.

    Solution


  45. Question

    Below is a 2-way table expressing joint probabilities.

    A not A
    B 19% 16%
    not B 31% 34%

    So,

    \[\begin{align} P(A \text{ and }B) &= 0.19 \\ P(A \text{ and not }B) &= 0.31 \\ P([\text{not }A] \text{ and }B) &= 0.16 \\ P([\text{not }A] \text{ and [not }B]) &= 0.34 \\ \end{align}\]

    Are events \(A\) and \(B\) independent?


    1. Yes, events A and B are independent.
    2. No, events A and B are dependent.

    Solution


  46. Question

    Below is a 2-way table expressing joint probabilities.

    A not A
    B 15% 5%
    not B 60% 20%

    So,

    \[\begin{align} P(A \text{ and }B) &= 0.15 \\ P(A \text{ and not }B) &= 0.6 \\ P([\text{not }A] \text{ and }B) &= 0.05 \\ P([\text{not }A] \text{ and [not }B]) &= 0.2 \\ \end{align}\]

    Are events \(A\) and \(B\) independent?


    1. Yes, events A and B are independent.
    2. No, events A and B are dependent.

    Solution


  47. Question

    Below is a 2-way table expressing joint probabilities.

    A not A
    B 30% 49%
    not B 10% 11%

    So,

    \[\begin{align} P(A \text{ and }B) &= 0.3 \\ P(A \text{ and not }B) &= 0.1 \\ P([\text{not }A] \text{ and }B) &= 0.49 \\ P([\text{not }A] \text{ and [not }B]) &= 0.11 \\ \end{align}\]

    Are events \(A\) and \(B\) independent?


    1. Yes, events A and B are independent.
    2. No, events A and B are dependent.

    Solution


  48. Question

    Below is a 2-way table expressing joint probabilities.

    A not A
    B 6% 14%
    not B 24% 56%

    So,

    \[\begin{align} P(A \text{ and }B) &= 0.06 \\ P(A \text{ and not }B) &= 0.24 \\ P([\text{not }A] \text{ and }B) &= 0.14 \\ P([\text{not }A] \text{ and [not }B]) &= 0.56 \\ \end{align}\]

    Are events \(A\) and \(B\) independent?


    1. Yes, events A and B are independent.
    2. No, events A and B are dependent.

    Solution


  49. Question

    Below is a 2-way table expressing joint probabilities.

    A not A
    B 36% 39%
    not B 12% 13%

    So,

    \[\begin{align} P(A \text{ and }B) &= 0.36 \\ P(A \text{ and not }B) &= 0.12 \\ P([\text{not }A] \text{ and }B) &= 0.39 \\ P([\text{not }A] \text{ and [not }B]) &= 0.13 \\ \end{align}\]

    Are events \(A\) and \(B\) independent?


    1. Yes, events A and B are independent.
    2. No, events A and B are dependent.

    Solution


  50. Question

    Below is a 2-way table expressing joint probabilities.

    A not A
    B 12% 11%
    not B 36% 41%

    So,

    \[\begin{align} P(A \text{ and }B) &= 0.12 \\ P(A \text{ and not }B) &= 0.36 \\ P([\text{not }A] \text{ and }B) &= 0.11 \\ P([\text{not }A] \text{ and [not }B]) &= 0.41 \\ \end{align}\]

    Are events \(A\) and \(B\) independent?


    1. Yes, events A and B are independent.
    2. No, events A and B are dependent.

    Solution


  51. Question

    Below are 4 exponential functions.

    \[\begin{align} A(x) ~&=~ 10.7\cdot\left(\frac{37}{17}\right)^{-1.57x} \\\\ B(x) ~&=~ 92.4\cdot\left(\frac{23}{5}\right)^{0.89x} \\\\ C(x) ~&=~ 55.6\cdot\left(\frac{3}{31}\right)^{-1.38x} \\\\ D(x) ~&=~ 55.4\cdot\left(\frac{13}{29}\right)^{-0.38x} \end{align}\]

    Which function represents exponential decay?


    1. A
    2. B
    3. C
    4. D

    Solution


  52. Question

    Below are 4 exponential functions.

    \[\begin{align} A(x) ~&=~ 22.2\cdot\left(\frac{11}{5}\right)^{0.44x} \\\\ B(x) ~&=~ 73.3\cdot\left(\frac{3}{23}\right)^{0.58x} \\\\ C(x) ~&=~ 17.7\cdot\left(\frac{17}{2}\right)^{0.81x} \\\\ D(x) ~&=~ 53.3\cdot\left(\frac{13}{19}\right)^{-0.42x} \end{align}\]

    Which function represents exponential decay?


    1. A
    2. B
    3. C
    4. D

    Solution


  53. Question

    Below are 4 exponential functions.

    \[\begin{align} A(x) ~&=~ 33.3\cdot\left(\frac{13}{5}\right)^{-1.21x} \\\\ B(x) ~&=~ 82.9\cdot\left(\frac{3}{31}\right)^{-1.2x} \\\\ C(x) ~&=~ 27\cdot\left(\frac{37}{17}\right)^{0.26x} \\\\ D(x) ~&=~ 56.4\cdot\left(\frac{7}{23}\right)^{-0.71x} \end{align}\]

    Which function represents exponential decay?


    1. A
    2. B
    3. C
    4. D

    Solution


  54. Question

    Below are 4 exponential functions.

    \[\begin{align} A(x) ~&=~ 42.1\cdot\left(\frac{2}{23}\right)^{-1.9x} \\\\ B(x) ~&=~ 95.5\cdot\left(\frac{7}{3}\right)^{1.9x} \\\\ C(x) ~&=~ 45.1\cdot\left(\frac{29}{37}\right)^{0.67x} \\\\ D(x) ~&=~ 55.1\cdot\left(\frac{13}{17}\right)^{-1.78x} \end{align}\]

    Which function represents exponential decay?


    1. A
    2. B
    3. C
    4. D

    Solution


  55. Question

    Below are 4 exponential functions.

    \[\begin{align} A(x) ~&=~ 77\cdot\left(\frac{31}{3}\right)^{1.82x} \\\\ B(x) ~&=~ 47.5\cdot\left(\frac{17}{5}\right)^{1.98x} \\\\ C(x) ~&=~ 84.6\cdot\left(\frac{29}{19}\right)^{1.69x} \\\\ D(x) ~&=~ 21\cdot\left(\frac{23}{7}\right)^{-1.13x} \end{align}\]

    Which function represents exponential decay?


    1. A
    2. B
    3. C
    4. D

    Solution


  56. Question

    Below are 4 exponential functions.

    \[\begin{align} A(x) ~&=~ 94.1\cdot\left(\frac{7}{2}\right)^{0.22x} \\\\ B(x) ~&=~ 10.8\cdot\left(\frac{17}{23}\right)^{0.34x} \\\\ C(x) ~&=~ 81.8\cdot\left(\frac{29}{37}\right)^{-0.72x} \\\\ D(x) ~&=~ 71.7\cdot\left(\frac{31}{19}\right)^{1.25x} \end{align}\]

    Which function represents exponential decay?


    1. A
    2. B
    3. C
    4. D

    Solution


  57. Question

    Below are 4 exponential functions.

    \[\begin{align} A(x) ~&=~ 78.5\cdot\left(\frac{19}{23}\right)^{1.37x} \\\\ B(x) ~&=~ 89.7\cdot\left(\frac{29}{37}\right)^{-0.83x} \\\\ C(x) ~&=~ 32.3\cdot\left(\frac{5}{2}\right)^{0.72x} \\\\ D(x) ~&=~ 37.9\cdot\left(\frac{7}{31}\right)^{-0.29x} \end{align}\]

    Which function represents exponential decay?


    1. A
    2. B
    3. C
    4. D

    Solution


  58. Question

    Below are 4 exponential functions.

    \[\begin{align} A(x) ~&=~ 88.5\cdot\left(\frac{7}{29}\right)^{0.24x} \\\\ B(x) ~&=~ 48.3\cdot\left(\frac{5}{31}\right)^{-0.27x} \\\\ C(x) ~&=~ 72.3\cdot\left(\frac{13}{23}\right)^{-1.77x} \\\\ D(x) ~&=~ 76.4\cdot\left(\frac{11}{19}\right)^{-1.69x} \end{align}\]

    Which function represents exponential decay?


    1. A
    2. B
    3. C
    4. D

    Solution


  59. Question

    Below are 4 exponential functions.

    \[\begin{align} A(x) ~&=~ 73.9\cdot\left(\frac{5}{37}\right)^{-1.22x} \\\\ B(x) ~&=~ 32.3\cdot\left(\frac{29}{19}\right)^{0.34x} \\\\ C(x) ~&=~ 90.6\cdot\left(\frac{13}{17}\right)^{1.2x} \\\\ D(x) ~&=~ 40.7\cdot\left(\frac{31}{3}\right)^{1.5x} \end{align}\]

    Which function represents exponential decay?


    1. A
    2. B
    3. C
    4. D

    Solution


  60. Question

    Below are 4 exponential functions.

    \[\begin{align} A(x) ~&=~ 93.4\cdot\left(\frac{19}{13}\right)^{1.4x} \\\\ B(x) ~&=~ 68.1\cdot\left(\frac{7}{37}\right)^{-1.94x} \\\\ C(x) ~&=~ 33.1\cdot\left(\frac{23}{3}\right)^{1.33x} \\\\ D(x) ~&=~ 69.9\cdot\left(\frac{11}{31}\right)^{0.19x} \end{align}\]

    Which function represents exponential decay?


    1. A
    2. B
    3. C
    4. D

    Solution


  61. Question

    Let function \(f\) be defined with the algebraic formula below: \[f(x) = \frac{x}{8}-3\]

    Find an expression for the inverse function \(f^{-1}\).


    1. \(f^{-1}(x)~=~\frac{x}{3}+8\)
    2. \(f^{-1}(x)~=~8(x-3)\)
    3. \(f^{-1}(x)~=~8(x+3)\)
    4. \(f^{-1}(x)~=~3x+8\)

    Solution


  62. Question

    Let function \(f\) be defined with the algebraic formula below: \[f(x) = 8x+5\]

    Find an expression for the inverse function \(f^{-1}\).


    1. \(f^{-1}(x)~=~8(x+5)\)
    2. \(f^{-1}(x)~=~\frac{x}{5}+8\)
    3. \(f^{-1}(x)~=~\frac{x-5}{8}\)
    4. \(f^{-1}(x)~=~\frac{x+5}{8}\)

    Solution


  63. Question

    Let function \(f\) be defined with the algebraic formula below: \[f(x) = 3x+4\]

    Find an expression for the inverse function \(f^{-1}\).


    1. \(f^{-1}(x)~=~\frac{x}{4}-3\)
    2. \(f^{-1}(x)~=~\frac{x-4}{3}\)
    3. \(f^{-1}(x)~=~4x-3\)
    4. \(f^{-1}(x)~=~4x+3\)

    Solution


  64. Question

    Let function \(f\) be defined with the algebraic formula below: \[f(x) = \frac{x}{5}-4\]

    Find an expression for the inverse function \(f^{-1}\).


    1. \(f^{-1}(x)~=~5(x+4)\)
    2. \(f^{-1}(x)~=~\frac{x}{4}-5\)
    3. \(f^{-1}(x)~=~\frac{x-4}{5}\)
    4. \(f^{-1}(x)~=~4x-5\)

    Solution


  65. Question

    Let function \(f\) be defined with the algebraic formula below: \[f(x) = 4x-3\]

    Find an expression for the inverse function \(f^{-1}\).


    1. \(f^{-1}(x)~=~4(x-3)\)
    2. \(f^{-1}(x)~=~\frac{x+3}{4}\)
    3. \(f^{-1}(x)~=~\frac{x}{3}-4\)
    4. \(f^{-1}(x)~=~\frac{x}{3}+4\)

    Solution


  66. Question

    Let function \(f\) be defined with the algebraic formula below: \[f(x) = 6x-7\]

    Find an expression for the inverse function \(f^{-1}\).


    1. \(f^{-1}(x)~=~\frac{x+7}{6}\)
    2. \(f^{-1}(x)~=~\frac{x}{7}-6\)
    3. \(f^{-1}(x)~=~\frac{x-7}{6}\)
    4. \(f^{-1}(x)~=~6(x-7)\)

    Solution


  67. Question

    Let function \(f\) be defined with the algebraic formula below: \[f(x) = \frac{x-9}{5}\]

    Find an expression for the inverse function \(f^{-1}\).


    1. \(f^{-1}(x)~=~9(x-5)\)
    2. \(f^{-1}(x)~=~\frac{x+5}{9}\)
    3. \(f^{-1}(x)~=~\frac{x-5}{9}\)
    4. \(f^{-1}(x)~=~5x+9\)

    Solution


  68. Question

    Let function \(f\) be defined with the algebraic formula below: \[f(x) = \frac{x}{3}-9\]

    Find an expression for the inverse function \(f^{-1}\).


    1. \(f^{-1}(x)~=~3(x+9)\)
    2. \(f^{-1}(x)~=~\frac{x}{9}-3\)
    3. \(f^{-1}(x)~=~3(x-9)\)
    4. \(f^{-1}(x)~=~9x-3\)

    Solution


  69. Question

    Let function \(f\) be defined with the algebraic formula below: \[f(x) = \frac{x}{9}+5\]

    Find an expression for the inverse function \(f^{-1}\).


    1. \(f^{-1}(x)~=~\frac{x-5}{9}\)
    2. \(f^{-1}(x)~=~9(x-5)\)
    3. \(f^{-1}(x)~=~\frac{x}{5}-9\)
    4. \(f^{-1}(x)~=~9(x+5)\)

    Solution


  70. Question

    Let function \(f\) be defined with the algebraic formula below: \[f(x) = 6(x+5)\]

    Find an expression for the inverse function \(f^{-1}\).


    1. \(f^{-1}(x)~=~\frac{x}{6}+5\)
    2. \(f^{-1}(x)~=~\frac{x}{6}-5\)
    3. \(f^{-1}(x)~=~\frac{x+6}{5}\)
    4. \(f^{-1}(x)~=~\frac{x-6}{5}\)

    Solution


  71. Question

    Which of the following has \(9+8i\) as a solution?

    (A) \(~~0=x^2+18x+145\)

    (B) \(~~0=x^2+18x-145\)

    (C) \(~~0=x^2-18x-145\)

    (D) \(~~0=x^2-18x+145\)


    1. A
    2. B
    3. C
    4. D

    Solution


  72. Question

    Which of the following has \(6+3i\) as a solution?

    (A) \(~~0=x^2+12x+45\)

    (B) \(~~0=x^2+12x-45\)

    (C) \(~~0=x^2-12x+45\)

    (D) \(~~0=x^2-12x-45\)


    1. A
    2. B
    3. C
    4. D

    Solution


  73. Question

    Which of the following has \(-1+8i\) as a solution?

    (A) \(~~0=x^2+2x-65\)

    (B) \(~~0=x^2+2x+65\)

    (C) \(~~0=x^2-2x+65\)

    (D) \(~~0=x^2-2x-65\)


    1. A
    2. B
    3. C
    4. D

    Solution


  74. Question

    Which of the following has \(8-7i\) as a solution?

    (A) \(~~0=x^2+16x+113\)

    (B) \(~~0=x^2-16x+113\)

    (C) \(~~0=x^2-16x-113\)

    (D) \(~~0=x^2+16x-113\)


    1. A
    2. B
    3. C
    4. D

    Solution


  75. Question

    Which of the following has \(1+i\) as a solution?

    (A) \(~~0=x^2-2x+2\)

    (B) \(~~0=x^2-2x-2\)

    (C) \(~~0=x^2+2x-2\)

    (D) \(~~0=x^2+2x+2\)


    1. A
    2. B
    3. C
    4. D

    Solution


  76. Question

    Which of the following has \(3+7i\) as a solution?

    (A) \(~~0=x^2+6x+58\)

    (B) \(~~0=x^2+6x-58\)

    (C) \(~~0=x^2-6x-58\)

    (D) \(~~0=x^2-6x+58\)


    1. A
    2. B
    3. C
    4. D

    Solution


  77. Question

    Which of the following has \(-2-5i\) as a solution?

    (A) \(~~0=x^2-4x+29\)

    (B) \(~~0=x^2+4x+29\)

    (C) \(~~0=x^2-4x-29\)

    (D) \(~~0=x^2+4x-29\)


    1. A
    2. B
    3. C
    4. D

    Solution


  78. Question

    Which of the following has \(1-3i\) as a solution?

    (A) \(~~0=x^2-2x-10\)

    (B) \(~~0=x^2-2x+10\)

    (C) \(~~0=x^2+2x-10\)

    (D) \(~~0=x^2+2x+10\)


    1. A
    2. B
    3. C
    4. D

    Solution


  79. Question

    Which of the following has \(5+4i\) as a solution?

    (A) \(~~0=x^2+10x-41\)

    (B) \(~~0=x^2-10x+41\)

    (C) \(~~0=x^2+10x+41\)

    (D) \(~~0=x^2-10x-41\)


    1. A
    2. B
    3. C
    4. D

    Solution


  80. Question

    Which of the following has \(-3-i\) as a solution?

    (A) \(~~0=x^2+6x+10\)

    (B) \(~~0=x^2-6x+10\)

    (C) \(~~0=x^2-6x-10\)

    (D) \(~~0=x^2+6x-10\)


    1. A
    2. B
    3. C
    4. D

    Solution


  81. Question

    Simplify the quotient of complex numbers by rationalizing the denominator.

    \[\frac{2-i}{6+3i}\]

    Your answer (when simplified) will have the form \[\frac{a+bi}{c}\] If \(c>0\), what are the values of \(a\), \(b\), and \(c\)?



    Solution


  82. Question

    Simplify the quotient of complex numbers by rationalizing the denominator.

    \[\frac{5-7i}{6+3i}\]

    Your answer (when simplified) will have the form \[\frac{a+bi}{c}\] If \(c>0\), what are the values of \(a\), \(b\), and \(c\)?



    Solution


  83. Question

    Simplify the quotient of complex numbers by rationalizing the denominator.

    \[\frac{-8-3i}{-1+2i}\]

    Your answer (when simplified) will have the form \[\frac{a+bi}{c}\] If \(c>0\), what are the values of \(a\), \(b\), and \(c\)?



    Solution


  84. Question

    Simplify the quotient of complex numbers by rationalizing the denominator.

    \[\frac{-4-7i}{9+2i}\]

    Your answer (when simplified) will have the form \[\frac{a+bi}{c}\] If \(c>0\), what are the values of \(a\), \(b\), and \(c\)?



    Solution


  85. Question

    Simplify the quotient of complex numbers by rationalizing the denominator.

    \[\frac{1-5i}{2+4i}\]

    Your answer (when simplified) will have the form \[\frac{a+bi}{c}\] If \(c>0\), what are the values of \(a\), \(b\), and \(c\)?



    Solution


  86. Question

    Simplify the quotient of complex numbers by rationalizing the denominator.

    \[\frac{6-4i}{3+i}\]

    Your answer (when simplified) will have the form \[\frac{a+bi}{c}\] If \(c>0\), what are the values of \(a\), \(b\), and \(c\)?



    Solution


  87. Question

    Simplify the quotient of complex numbers by rationalizing the denominator.

    \[\frac{5+7i}{2+6i}\]

    Your answer (when simplified) will have the form \[\frac{a+bi}{c}\] If \(c>0\), what are the values of \(a\), \(b\), and \(c\)?



    Solution


  88. Question

    Simplify the quotient of complex numbers by rationalizing the denominator.

    \[\frac{-7-4i}{-3+i}\]

    Your answer (when simplified) will have the form \[\frac{a+bi}{c}\] If \(c>0\), what are the values of \(a\), \(b\), and \(c\)?



    Solution


  89. Question

    Simplify the quotient of complex numbers by rationalizing the denominator.

    \[\frac{1+9i}{-2+6i}\]

    Your answer (when simplified) will have the form \[\frac{a+bi}{c}\] If \(c>0\), what are the values of \(a\), \(b\), and \(c\)?



    Solution


  90. Question

    Simplify the quotient of complex numbers by rationalizing the denominator.

    \[\frac{-8+4i}{9+3i}\]

    Your answer (when simplified) will have the form \[\frac{a+bi}{c}\] If \(c>0\), what are the values of \(a\), \(b\), and \(c\)?



    Solution


  91. Question

    In Chemistry, the pH is used to measure the acidity of a solution. The pH is calculated from the concentration of hydrogen ions (in moles per liter).

    \[\mathrm{pH} = -\log_{10}\big(\left[\mathrm{H^{+}}\right]\big)\]

    The table below lists the (rounded) base-10 logarithm of integers between 1 and 9.

    \(x\) \(\log_{10}(x)\)
    1 0.000
    2 0.301
    3 0.477
    4 0.602
    5 0.699
    6 0.778
    7 0.845
    8 0.903
    9 0.954

    If the concentration of hydrogen ions is \(\left[\mathrm{H^{+}}\right]=8\cdot 10^{-11}\) moles per liter, what is the pH? Please use the table, and do not round your answer any more than the table already has.


    Solution


  92. Question

    In Chemistry, the pH is used to measure the acidity of a solution. The pH is calculated from the concentration of hydrogen ions (in moles per liter).

    \[\mathrm{pH} = -\log_{10}\big(\left[\mathrm{H^{+}}\right]\big)\]

    The table below lists the (rounded) base-10 logarithm of integers between 1 and 9.

    \(x\) \(\log_{10}(x)\)
    1 0.000
    2 0.301
    3 0.477
    4 0.602
    5 0.699
    6 0.778
    7 0.845
    8 0.903
    9 0.954

    If the concentration of hydrogen ions is \(\left[\mathrm{H^{+}}\right]=5\cdot 10^{-1}\) moles per liter, what is the pH? Please use the table, and do not round your answer any more than the table already has.


    Solution


  93. Question

    In Chemistry, the pH is used to measure the acidity of a solution. The pH is calculated from the concentration of hydrogen ions (in moles per liter).

    \[\mathrm{pH} = -\log_{10}\big(\left[\mathrm{H^{+}}\right]\big)\]

    The table below lists the (rounded) base-10 logarithm of integers between 1 and 9.

    \(x\) \(\log_{10}(x)\)
    1 0.000
    2 0.301
    3 0.477
    4 0.602
    5 0.699
    6 0.778
    7 0.845
    8 0.903
    9 0.954

    If the concentration of hydrogen ions is \(\left[\mathrm{H^{+}}\right]=9\cdot 10^{-1}\) moles per liter, what is the pH? Please use the table, and do not round your answer any more than the table already has.


    Solution


  94. Question

    In Chemistry, the pH is used to measure the acidity of a solution. The pH is calculated from the concentration of hydrogen ions (in moles per liter).

    \[\mathrm{pH} = -\log_{10}\big(\left[\mathrm{H^{+}}\right]\big)\]

    The table below lists the (rounded) base-10 logarithm of integers between 1 and 9.

    \(x\) \(\log_{10}(x)\)
    1 0.000
    2 0.301
    3 0.477
    4 0.602
    5 0.699
    6 0.778
    7 0.845
    8 0.903
    9 0.954

    If the concentration of hydrogen ions is \(\left[\mathrm{H^{+}}\right]=5\cdot 10^{-2}\) moles per liter, what is the pH? Please use the table, and do not round your answer any more than the table already has.


    Solution


  95. Question

    In Chemistry, the pH is used to measure the acidity of a solution. The pH is calculated from the concentration of hydrogen ions (in moles per liter).

    \[\mathrm{pH} = -\log_{10}\big(\left[\mathrm{H^{+}}\right]\big)\]

    The table below lists the (rounded) base-10 logarithm of integers between 1 and 9.

    \(x\) \(\log_{10}(x)\)
    1 0.000
    2 0.301
    3 0.477
    4 0.602
    5 0.699
    6 0.778
    7 0.845
    8 0.903
    9 0.954

    If the concentration of hydrogen ions is \(\left[\mathrm{H^{+}}\right]=4\cdot 10^{-6}\) moles per liter, what is the pH? Please use the table, and do not round your answer any more than the table already has.


    Solution


  96. Question

    In Chemistry, the pH is used to measure the acidity of a solution. The pH is calculated from the concentration of hydrogen ions (in moles per liter).

    \[\mathrm{pH} = -\log_{10}\big(\left[\mathrm{H^{+}}\right]\big)\]

    The table below lists the (rounded) base-10 logarithm of integers between 1 and 9.

    \(x\) \(\log_{10}(x)\)
    1 0.000
    2 0.301
    3 0.477
    4 0.602
    5 0.699
    6 0.778
    7 0.845
    8 0.903
    9 0.954

    If the concentration of hydrogen ions is \(\left[\mathrm{H^{+}}\right]=5\cdot 10^{-12}\) moles per liter, what is the pH? Please use the table, and do not round your answer any more than the table already has.


    Solution


  97. Question

    In Chemistry, the pH is used to measure the acidity of a solution. The pH is calculated from the concentration of hydrogen ions (in moles per liter).

    \[\mathrm{pH} = -\log_{10}\big(\left[\mathrm{H^{+}}\right]\big)\]

    The table below lists the (rounded) base-10 logarithm of integers between 1 and 9.

    \(x\) \(\log_{10}(x)\)
    1 0.000
    2 0.301
    3 0.477
    4 0.602
    5 0.699
    6 0.778
    7 0.845
    8 0.903
    9 0.954

    If the concentration of hydrogen ions is \(\left[\mathrm{H^{+}}\right]=9\cdot 10^{-9}\) moles per liter, what is the pH? Please use the table, and do not round your answer any more than the table already has.


    Solution


  98. Question

    In Chemistry, the pH is used to measure the acidity of a solution. The pH is calculated from the concentration of hydrogen ions (in moles per liter).

    \[\mathrm{pH} = -\log_{10}\big(\left[\mathrm{H^{+}}\right]\big)\]

    The table below lists the (rounded) base-10 logarithm of integers between 1 and 9.

    \(x\) \(\log_{10}(x)\)
    1 0.000
    2 0.301
    3 0.477
    4 0.602
    5 0.699
    6 0.778
    7 0.845
    8 0.903
    9 0.954

    If the concentration of hydrogen ions is \(\left[\mathrm{H^{+}}\right]=4\cdot 10^{-2}\) moles per liter, what is the pH? Please use the table, and do not round your answer any more than the table already has.


    Solution


  99. Question

    In Chemistry, the pH is used to measure the acidity of a solution. The pH is calculated from the concentration of hydrogen ions (in moles per liter).

    \[\mathrm{pH} = -\log_{10}\big(\left[\mathrm{H^{+}}\right]\big)\]

    The table below lists the (rounded) base-10 logarithm of integers between 1 and 9.

    \(x\) \(\log_{10}(x)\)
    1 0.000
    2 0.301
    3 0.477
    4 0.602
    5 0.699
    6 0.778
    7 0.845
    8 0.903
    9 0.954

    If the concentration of hydrogen ions is \(\left[\mathrm{H^{+}}\right]=4\cdot 10^{-8}\) moles per liter, what is the pH? Please use the table, and do not round your answer any more than the table already has.


    Solution


  100. Question

    In Chemistry, the pH is used to measure the acidity of a solution. The pH is calculated from the concentration of hydrogen ions (in moles per liter).

    \[\mathrm{pH} = -\log_{10}\big(\left[\mathrm{H^{+}}\right]\big)\]

    The table below lists the (rounded) base-10 logarithm of integers between 1 and 9.

    \(x\) \(\log_{10}(x)\)
    1 0.000
    2 0.301
    3 0.477
    4 0.602
    5 0.699
    6 0.778
    7 0.845
    8 0.903
    9 0.954

    If the concentration of hydrogen ions is \(\left[\mathrm{H^{+}}\right]=9\cdot 10^{-13}\) moles per liter, what is the pH? Please use the table, and do not round your answer any more than the table already has.


    Solution


  101. Question

    You can verify the exponential relationship below. \[4^{3} = 64\]

    These same three numbers can be used to satisfy the following logarithmic equation.

    \[\log_{a}(b) = c\]

    Determine values for \(a\), \(b\), and \(c\).



    Solution


  102. Question

    You can verify the exponential relationship below. \[6^{3} = 216\]

    These same three numbers can be used to satisfy the following logarithmic equation.

    \[\log_{a}(b) = c\]

    Determine values for \(a\), \(b\), and \(c\).



    Solution


  103. Question

    You can verify the exponential relationship below. \[3^{8} = 6561\]

    These same three numbers can be used to satisfy the following logarithmic equation.

    \[\log_{a}(b) = c\]

    Determine values for \(a\), \(b\), and \(c\).



    Solution


  104. Question

    You can verify the exponential relationship below. \[7^{3} = 343\]

    These same three numbers can be used to satisfy the following logarithmic equation.

    \[\log_{a}(b) = c\]

    Determine values for \(a\), \(b\), and \(c\).



    Solution


  105. Question

    You can verify the exponential relationship below. \[6^{2} = 36\]

    These same three numbers can be used to satisfy the following logarithmic equation.

    \[\log_{a}(b) = c\]

    Determine values for \(a\), \(b\), and \(c\).



    Solution


  106. Question

    You can verify the exponential relationship below. \[8^{2} = 64\]

    These same three numbers can be used to satisfy the following logarithmic equation.

    \[\log_{a}(b) = c\]

    Determine values for \(a\), \(b\), and \(c\).



    Solution


  107. Question

    You can verify the exponential relationship below. \[9^{4} = 6561\]

    These same three numbers can be used to satisfy the following logarithmic equation.

    \[\log_{a}(b) = c\]

    Determine values for \(a\), \(b\), and \(c\).



    Solution


  108. Question

    You can verify the exponential relationship below. \[4^{6} = 4096\]

    These same three numbers can be used to satisfy the following logarithmic equation.

    \[\log_{a}(b) = c\]

    Determine values for \(a\), \(b\), and \(c\).



    Solution


  109. Question

    You can verify the exponential relationship below. \[10^{2} = 100\]

    These same three numbers can be used to satisfy the following logarithmic equation.

    \[\log_{a}(b) = c\]

    Determine values for \(a\), \(b\), and \(c\).



    Solution


  110. Question

    You can verify the exponential relationship below. \[4^{5} = 1024\]

    These same three numbers can be used to satisfy the following logarithmic equation.

    \[\log_{a}(b) = c\]

    Determine values for \(a\), \(b\), and \(c\).



    Solution


  111. Question

    In a school, there are 84 students. Each student can be in bike club, crochet club, both, or neither. The amounts are represented in the Venn diagram below.

    plot of chunk unnamed-chunk-2

    Let \(B\) represent the event that a randomly selected student is in bike club, and let \(C\) represent the event that a random student is in crochet club.



    Solution


  112. Question

    In a school, there are 131 students. Each student can be in bike club, crochet club, both, or neither. The amounts are represented in the Venn diagram below.

    plot of chunk unnamed-chunk-2

    Let \(B\) represent the event that a randomly selected student is in bike club, and let \(C\) represent the event that a random student is in crochet club.



    Solution


  113. Question

    In a school, there are 129 students. Each student can be in bike club, crochet club, both, or neither. The amounts are represented in the Venn diagram below.

    plot of chunk unnamed-chunk-2

    Let \(B\) represent the event that a randomly selected student is in bike club, and let \(C\) represent the event that a random student is in crochet club.



    Solution


  114. Question

    In a school, there are 66 students. Each student can be in bike club, crochet club, both, or neither. The amounts are represented in the Venn diagram below.

    plot of chunk unnamed-chunk-2

    Let \(B\) represent the event that a randomly selected student is in bike club, and let \(C\) represent the event that a random student is in crochet club.



    Solution


  115. Question

    In a school, there are 114 students. Each student can be in bike club, crochet club, both, or neither. The amounts are represented in the Venn diagram below.

    plot of chunk unnamed-chunk-2

    Let \(B\) represent the event that a randomly selected student is in bike club, and let \(C\) represent the event that a random student is in crochet club.



    Solution


  116. Question

    In a school, there are 72 students. Each student can be in bike club, crochet club, both, or neither. The amounts are represented in the Venn diagram below.

    plot of chunk unnamed-chunk-2

    Let \(B\) represent the event that a randomly selected student is in bike club, and let \(C\) represent the event that a random student is in crochet club.



    Solution


  117. Question

    In a school, there are 78 students. Each student can be in bike club, crochet club, both, or neither. The amounts are represented in the Venn diagram below.

    plot of chunk unnamed-chunk-2

    Let \(B\) represent the event that a randomly selected student is in bike club, and let \(C\) represent the event that a random student is in crochet club.



    Solution


  118. Question

    In a school, there are 100 students. Each student can be in bike club, crochet club, both, or neither. The amounts are represented in the Venn diagram below.

    plot of chunk unnamed-chunk-2

    Let \(B\) represent the event that a randomly selected student is in bike club, and let \(C\) represent the event that a random student is in crochet club.



    Solution


  119. Question

    In a school, there are 77 students. Each student can be in bike club, crochet club, both, or neither. The amounts are represented in the Venn diagram below.

    plot of chunk unnamed-chunk-2

    Let \(B\) represent the event that a randomly selected student is in bike club, and let \(C\) represent the event that a random student is in crochet club.



    Solution


  120. Question

    In a school, there are 53 students. Each student can be in bike club, crochet club, both, or neither. The amounts are represented in the Venn diagram below.

    plot of chunk unnamed-chunk-2

    Let \(B\) represent the event that a randomly selected student is in bike club, and let \(C\) represent the event that a random student is in crochet club.



    Solution


  121. Question

    The inner dimensions of a frame are 40 inches by 28 inches. An artist hopes to print an image with an aspect ratio of 2.05 such that a uniformly wide mat fits around the image.

    plot of chunk unnamed-chunk-2

    Find \(b\), the width of the mat in inches. The tolerance is \(\pm 0.01\) inches.


    Solution


  122. Question

    The inner dimensions of a frame are 32 inches by 18 inches. An artist hopes to print an image with an aspect ratio of 2.58 such that a uniformly wide mat fits around the image.

    plot of chunk unnamed-chunk-2

    Find \(b\), the width of the mat in inches. The tolerance is \(\pm 0.01\) inches.


    Solution


  123. Question

    The inner dimensions of a frame are 25 inches by 18 inches. An artist hopes to print an image with an aspect ratio of 1.75 such that a uniformly wide mat fits around the image.

    plot of chunk unnamed-chunk-2

    Find \(b\), the width of the mat in inches. The tolerance is \(\pm 0.01\) inches.


    Solution


  124. Question

    The inner dimensions of a frame are 36 inches by 21 inches. An artist hopes to print an image with an aspect ratio of 2.24 such that a uniformly wide mat fits around the image.

    plot of chunk unnamed-chunk-2

    Find \(b\), the width of the mat in inches. The tolerance is \(\pm 0.01\) inches.


    Solution


  125. Question

    The inner dimensions of a frame are 19 inches by 14 inches. An artist hopes to print an image with an aspect ratio of 1.65 such that a uniformly wide mat fits around the image.

    plot of chunk unnamed-chunk-2

    Find \(b\), the width of the mat in inches. The tolerance is \(\pm 0.01\) inches.


    Solution


  126. Question

    The inner dimensions of a frame are 34 inches by 28 inches. An artist hopes to print an image with an aspect ratio of 1.26 such that a uniformly wide mat fits around the image.

    plot of chunk unnamed-chunk-2

    Find \(y\), the height of the image in inches. The tolerance is \(\pm 0.01\) inches.


    Solution


  127. Question

    The inner dimensions of a frame are 33 inches by 14 inches. An artist hopes to print an image with an aspect ratio of 3.2 such that a uniformly wide mat fits around the image.

    plot of chunk unnamed-chunk-2

    Find \(y\), the height of the image in inches. The tolerance is \(\pm 0.01\) inches.


    Solution


  128. Question

    The inner dimensions of a frame are 40 inches by 20 inches. An artist hopes to print an image with an aspect ratio of 2.28 such that a uniformly wide mat fits around the image.

    plot of chunk unnamed-chunk-2

    Find \(b\), the width of the mat in inches. The tolerance is \(\pm 0.01\) inches.


    Solution


  129. Question

    The inner dimensions of a frame are 31 inches by 21 inches. An artist hopes to print an image with an aspect ratio of 1.59 such that a uniformly wide mat fits around the image.

    plot of chunk unnamed-chunk-2

    Find \(b\), the width of the mat in inches. The tolerance is \(\pm 0.01\) inches.


    Solution


  130. Question

    The inner dimensions of a frame are 22 inches by 17 inches. An artist hopes to print an image with an aspect ratio of 1.58 such that a uniformly wide mat fits around the image.

    plot of chunk unnamed-chunk-2

    Find \(y\), the height of the image in inches. The tolerance is \(\pm 0.01\) inches.


    Solution